The current tasks are simulating events which produce a top quark and anti-top quark pair. The top quark is the heaviest quark and studying the decay of the top and anti-top pair is very important as it allows us to measure with greater precision a large number of physics properties of other particles. You can find more information on the top quark here:

The names of the tasks mostly contain information on various parameters used in the simulation but the first part is normally the same:

mc: stands for Monte Carlo, which refers to the way we "throw the dice" at the start of the simulation to introduce the same randomness that nature gives us
15: we simulate the detector and the beam as it was in 2015 (it was essentially the same in 2016 so we keep 15)
13TeV: 13 Tera Electron Volts, or 13000000000000eV is the energy that the protons have inside the LHC beam when they are collided

I had guessed about the 13TeV, but not the rest. Are those simulations meant:

To simulate changes to the ATLAS detector which could help in the future getting more precise measurements of the decayed pair top quark - anti top quark, or
To simulate various decay hypothesis and test, for example, which hypothesis matches best with the measurements?

Could you also give some details on the meaning of those "hdamp517p5_nonallhad" and "BFilter_ckkw30"?